Problem: Solve for $x$ and $y$ using elimination. ${3x-3y = -27}$ ${-3x-2y = -23}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. $-5y = -50$ $\dfrac{-5y}{{-5}} = \dfrac{-50}{{-5}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {3x-3y = -27}\thinspace$ to find $x$ ${3x - 3}{(10)}{= -27}$ $3x-30 = -27$ $3x-30{+30} = -27{+30}$ $3x = 3$ $\dfrac{3x}{{3}} = \dfrac{3}{{3}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {-3x-2y = -23}\thinspace$ and get the same answer for $x$ : ${-3x - 2}{(10)}{= -23}$ ${x = 1}$